Chapter 1.10, Problem 1E

We find the “steepness,” or slope, of a line passing through two points by dividing the difference in the _____-coordinates of these points by the difference in the _____-coordinates. So the line passing through the points (0, 1) and (2, 5) has slope _____.

To determine

To evaluate: The formula and the value of slope of line passing through two points.

Answer to Problem 1E

The formula of slope of line is defines as two points by dividing the difference in the y-coordinates of these points by the difference in the x-coordinates and the slope of line passing through two given points is 2.

Explanation of Solution

Given:

Two points of line are $\left(0,1\right)$ and $\left(2,5\right)$.

Formula used:

Formula of slope of line passing through two points is, $m=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

Section1:

The formula of slope of line is defines as two points by dividing the difference in the y-coordinates of these points by the difference in the x-coordinates.

In the above formula, $y_2-y_1$ is the difference of y-coordinates of two points and $x_2-x_1$ is the difference of x-coordinates of two points.

Thus, the formula of slope of line is defines as two points by dividing the difference in the y-coordinates of these points by the difference in the x-coordinates.

Section2:

Substitute 5 for $y_2$, 1 for $y_1$, 2 for $x_2$ and 0 for $x_1$ in the above formula to get the value of slope,

$\begin{array}{c}m=\frac{5-1}{2-0}\\ =\frac{4}{2}\\ m=2\end{array}$

Thus, the slope of line passing through two given points is 2.